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# Discrete Choice Modeling

William Greene Stern School of Business New York University. Discrete Choice Modeling. Part 1. Introduction. Course Overview. Methodology Regression Basics Categorical Variables Modeling Binary Choices Models for Ordered Choice Models for Count Data Multinomial Choice.

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## Discrete Choice Modeling

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1. William Greene Stern School of Business New York University Discrete Choice Modeling

2. Part 1 Introduction

3. Course Overview • Methodology • Regression Basics • Categorical Variables • Modeling Binary Choices • Models for Ordered Choice • Models for Count Data • Multinomial Choice

4. The Sample and Measurement Population Measurement Theory Characteristics Behavior Patterns Choices

5. Inference Population Measurement Econometrics Characteristics Behavior Patterns Choices

6. Classical Inference Population Measurement Econometrics Characteristics Behavior Patterns Choices Imprecise inference about the entire population – sampling theory and asymptotics

7. Bayesian Inference Population Measurement Econometrics Characteristics Behavior Patterns Choices Sharp, ‘exact’ inference about only the sample – the ‘posterior’ density.

8. Econometric Frameworks • Nonparametric • Semiparametric • Parametric • Classical (Sampling Theory) • Bayesian • We will focus on classical inference methods

9. Issues in Model Building • Estimation • Coefficients • Interesting Partial Effects • Functional Form and Specification • Statistical Inference • Prediction • Individuals • Aggregates • Model Assessment and Evaluation

10. Regression Basics • The “MODEL” = conditional mean function • Modeling the mean • Modeling probabilities for discrete choice • Specification • Estimation – coefficients and partial effects • Hypothesis testing • Prediction… and Fit • Estimation Methods

11. Application: Health Care Usage German Health Care Usage Data, 7,293 Individuals, Varying Numbers of PeriodsVariables in the file areData downloaded from Journal of Applied Econometrics Archive. This is an unbalanced panel with 7,293 individuals. They can be used for regression, count models, binary choice, ordered choice, and bivariate binary choice.  This is a large data set.  There are altogether 27,326 observations.  The number of observations ranges from 1 to 7.  (Frequencies are: 1=1525, 2=2158, 3=825, 4=926, 5=1051, 6=1000, 7=987).  Note, the variable NUMOBS below tells how many observations there are for each person.  This variable is repeated in each row of the data for the person.  (Downloaded from the JAE Archive) DOCTOR = 1(Number of doctor visits > 0) HOSPITAL = 1(Number of hospital visits > 0) HSAT =  health satisfaction, coded 0 (low) - 10 (high)   DOCVIS =  number of doctor visits in last three months HOSPVIS =  number of hospital visits in last calendar yearPUBLIC =  insured in public health insurance = 1; otherwise = 0 ADDON =  insured by add-on insurance = 1; otherswise = 0 HHNINC =  household nominal monthly net income in German marks / 10000. (4 observations with income=0 were dropped)HHKIDS = children under age 16 in the household = 1; otherwise = 0 EDUC =  years of schooling AGE = age in years MARRIED = marital status EDUC = years of education

12. Household Income

13. Regression - Income ---------------------------------------------------------------------- Ordinary least squares regression ............ LHS=LOGINC Mean = -.92882 Standard deviation = .47948 Number of observs. = 887 Model size Parameters = 2 Degrees of freedom = 885 Residuals Sum of squares = 183.19359 Standard error of e = .45497 Fit R-squared = .10064 Adjusted R-squared = .09962 Model test F[ 1, 885] (prob) = 99.0(.0000) Diagnostic Log likelihood = -559.06527 Restricted(b=0) = -606.10609 Chi-sq [ 1] (prob) = 94.1(.0000) Info criter. LogAmemiya Prd. Crt. = -1.57279 Akaike Info. Criter. = -1.57279 Bayes Info. Criter. = -1.56200 --------+------------------------------------------------------------- Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Mean of X --------+------------------------------------------------------------- Constant| -1.71604*** .08057 -21.299 .0000 EDUC| .07176*** .00721 9.951 .0000 10.9707 --------+------------------------------------------------------------- Note: ***, **, * = Significance at 1%, 5%, 10% level. ----------------------------------------------------------------------

14. Specification and Functional Form ---------------------------------------------------------------------- Ordinary least squares regression ............ LHS=LOGINC Mean = -.92882 Standard deviation = .47948 Number of observs. = 887 Model size Parameters = 3 Degrees of freedom = 884 Residuals Sum of squares = 183.00347 Standard error of e = .45499 Fit R-squared = .10157 Adjusted R-squared = .09954 Model test F[ 2, 884] (prob) = 50.0(.0000) Diagnostic Log likelihood = -558.60477 Restricted(b=0) = -606.10609 Chi-sq [ 2] (prob) = 95.0(.0000) Info criter. LogAmemiya Prd. Crt. = -1.57158 Akaike Info. Criter. = -1.57158 Bayes Info. Criter. = -1.55538 --------+------------------------------------------------------------- Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Mean of X --------+------------------------------------------------------------- Constant| -1.68303*** .08763 -19.207 .0000 EDUC| .06993*** .00746 9.375 .0000 10.9707 FEMALE| -.03065 .03199 -.958 .3379 .42277 --------+-------------------------------------------------------------

15. Interesting Partial Effects ---------------------------------------------------------------------- Ordinary least squares regression ............ LHS=LOGINC Mean = -.92882 Standard deviation = .47948 Number of observs. = 887 Model size Parameters = 5 Degrees of freedom = 882 Residuals Sum of squares = 171.87964 Standard error of e = .44145 Fit R-squared = .15618 Adjusted R-squared = .15235 Model test F[ 4, 882] (prob) = 40.8(.0000) Diagnostic Log likelihood = -530.79258 Restricted(b=0) = -606.10609 Chi-sq [ 4] (prob) = 150.6(.0000) Info criter. LogAmemiya Prd. Crt. = -1.62978 Akaike Info. Criter. = -1.62978 Bayes Info. Criter. = -1.60279 --------+------------------------------------------------------------- Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Mean of X --------+------------------------------------------------------------- Constant| -5.26676*** .56499 -9.322 .0000 EDUC| .06469*** .00730 8.860 .0000 10.9707 FEMALE| -.03683 .03134 -1.175 .2399 .42277 AGE| .15567*** .02297 6.777 .0000 50.4780 AGE2| -.00161*** .00023 -7.014 .0000 2620.79 --------+-------------------------------------------------------------

16. Impact of Age on Income

17. Inference: Does the same model apply to men and women? *Subsample analyzed for this command is FEMALE = 0 Residuals Sum of squares = 90.80587 Number of observs. = 512 Fit R-squared = .16538 --------+------------------------------------------------------------- Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Mean of X --------+------------------------------------------------------------- Constant| -5.45890*** .67675 -8.066 .0000 EDUC| .06626*** .00836 7.924 .0000 11.4342 AGE| .15894*** .02789 5.699 .0000 49.3750 AGE2| -.00160*** .00028 -5.695 .0000 2514.12 --------+------------------------------------------------------------- *Subsample analyzed for this command is FEMALE = 1 Residuals Sum of squares = 79.45629 Number of observs. = 375 Fit R-squared = .14008 --------+------------------------------------------------------------- Constant| -4.10991*** 1.03733 -3.962 .0001 EDUC| .05850*** .01399 4.180 .0000 10.3378 AGE| .11707*** .04103 2.853 .0046 51.9840 AGE2| -.00129*** .00040 -3.210 .0014 2766.43 --------+------------------------------------------------------------- Residuals Sum of squares = 172.14877 Number of observs. = 887 Fit R-squared = .15486 --------+------------------------------------------------------------- Constant| -5.24401*** .56478 -9.285 .0000 EDUC| .06676*** .00709 9.418 .0000 10.9707 AGE| .15342*** .02290 6.701 .0000 50.4780 AGE2| -.00159*** .00023 -6.944 .0000 2620.79 --------+-------------------------------------------------------------

18. Frameworks • Discrete Outcomes • Binary Choices • Ordered Choices • Models for Counts • Multinomial Choice • Modeling Methods • Modeling the conditional mean • Modeling Probabilities

19. Binary Outcome

20. Self Reported Health Satisfaction

21. Count of Occurrences

22. Multinomial Unordered Choice

23. Categorical Variables • Observed outcomes • Inherently discrete: number of occurrences, e.g., family size • Implicitly continuous: The observed data are discrete by construction, e.g., revealed preferences; our main subject • Multinomial: The observed outcome indexes a set of unordered labeled choices. • Implications • For model building • For analysis and prediction of behavior

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